O oscilador harmônico singular revisitado
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The one-dimensional Schrödinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive singular oscillator exhibits an infinite number of acceptable solutions provided the parameter responsible for the singularity is greater than a certain critical value, in disagreement with the literature. The problem for the whole line exhibits a two-fold degeneracy in the case of the singular oscillator, and the intrusion of additional solutions in the case of a nonsingular oscillator. Additionally, it is shown that the solution of the singular oscillator can not be obtained from the nonsingular oscillator via perturbation theory. © The Sociedade Brasileira de Física.
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Collapse to the center, Degeneracy, Harmonic oscillator, Singular potential
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Português
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Revista Brasileira de Ensino de Fisica, v. 35, n. 3, 2013.
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